Introduction

Question

How to select superior soybean genotypes across locations and years (GxE interaction) according to Multitrait ideotype? (Simultaneous selection)

Hypothesis

Estimate probability of superior performance (Dias et al. 2022) across seasons and years and classify genotypes using Bayesian Probabilistic Selection Index (Chagas et al. 2025)

Goal

Important

Select superior soybean genotypes to grain yield, plant height and plant lodging using Bayesian probabilistic selection index (BPSI) (Chagas et al. 2025)

Material e Métodos

Ensaios experimentais
  • 14 locations
  • 6 years
  • 41 trials
  • 98 genotypes
  • 3 traits (Grain Yield, Plant Height, Plant Lodging)
  • Randomized complete block design (RCB)

Material e Métodos

Individual analyses

\[ \mathbf{y} = \mathbf{X_1b} + \mathbf{Z_1g} + \mathbf{\epsilon} \]

onde \(\mathbf{y}\) é o vetor das observações fenotípicas, \(\mathbf{b}\) é o vetor dos efeitos fixos de repetição, \(\mathbf{g}\) é o vetor dos efeitos aleatórios de genótipo e \(\mathbf{\epsilon}\) é o vetor dos efeitos residuais. \(\mathbf{X_1}\), \(\mathbf{X_2}\) e \(\mathbf{Z_1}\) são matrizes de incidência dos efeitos \(\mathbf{b}\) e \(\mathbf{g}\) respectivamente.

Material e Métodos

Herdabilidade

\[ h^2 = \sigma^2g / \sigma^2g + \sigma^2e \]

onde \(\sigma^2g\) é a variância genética e \(\sigma_e^2\) é a variância do erro.

Coeficiente de Variação Experimental

\[ CV = \frac{\sigma_e}{\mu} \times 100 \]

onde \(\mu\) é a média da característica.

Material e Métodos

Teste de razão de verossimilhança

\[LRT= −2 \times (Log𝐿 - Log L_𝑅)\]

onde \(L\) é o ponto máximo da função de verossimilhança restrita do modelo completo e \(L_R\) é o mesmo para o modelo reduzido, ou seja, sem o efeito a ser testado. O valor de LRT foi comparado com o valor tabulado com base na tabela qui-quadrado, a um grau de liberdade e probabilidade de 0,95.

Material and Methods

Bayesian model

\[ y_{jkhp} = \mu + t_h + l_k + b_{p(k)} + g_j + gl_{jk} + gt_{jh} + \varepsilon_{jkhp} \] where the \(y_{jkhp}\) is the phenotypic record of the \(j^{th}\) genotype, allocated in the $ p^{th}$block, in the \(k^{th}\) location and in the year \(t_{th}\). All other effects were previously defined but \(b_{p(k)}\), which is the effect of the \(p^{th}\) block in the \(k{th}\) location, and \(gl^{jk}\) , which correspond to the genotype-by-location interaction \(t_h\) and \(t_{jh}\) are the main effect of years and the genotypes-by-years interaction effect, respectively.

Material and Methods

Probability of superior performance

BPSI index uses the probability of superior performance to estimate the chance of a genotype being selected in multienvironmental trials (Dias et al. 2022).

\[ Pr\left({\hat{g}}_i \in \Omega \middle| y\right) = \frac{1}{s}\sum_{s=1}^{s} I \left({\hat{g}}_i^{(s)} \in \Omega \middle| y\right) \]

where \(\hat{g}_i\) is the genotypic value, \(\Omega\) is a subset of genotypes with superior performance and \(s\) represents each sample of posterior distribution.

Material and methods

Bayesian Probabilistic Selection Index

\[ BPSI_i = \sum_{m=1}^{t} \frac{RankProbSup^t}{\omega^t} \]

where \(t\) is the total number of traits evaluated \((m =1, 2,…,t)\) and \(\omega\) is a weight. Traits of greater interest will have larger \(\omega\). We used weight 2 for GY and weight 1 for PH and PL. The 10% best-ranked families were selected according to the BPSI.

Genotype T1(Rank) T2(Rank) T3(Rank) PSI
1 10 5 2 ∑ i.= 17
2 5 3 10 ∑ i.= 18
3 7 3 10 ∑ i.= 19

Resultados

Resultados

Resultados

Resultados

Resultados

Resultados

Perguntas?

  • josetchagas@usp.br
  • Obrigado!

Referências

Chagas, José Tiago Barroso, Kaio Olimpio das Graças Dias, Vinicius Quintão Carneiro, Lawrência Maria Conceição De Oliveira, Núbia Xavier Nunes, José Domingos Pereira Júnior, Pedro Crescêncio Souza Carneiro, and José Eustáquio de Souza Carneiro. 2025. “Bayesian Probabilistic Selection Index in the Selection of Common Bean Families.” Crop Science 65 (May): e70072. https://doi.org/10.1002/CSC2.70072.
Dias, Kaio O. G., Jhonathan P. R. dos Santos, Matheus D. Krause, Hans Peter Piepho, Lauro J. M. Guimarães, Maria M. Pastina, and Antonio A. F. Garcia. 2022. “Leveraging Probability Concepts for Cultivar Recommendation in Multi-Environment Trials.” Theoretical and Applied Genetics 135 (April): 1385–99. https://doi.org/10.1007/S00122-022-04041-Y/FIGURES/4.